Transcription of Affine Transformations - Clemson University
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Affine Transformations - Clemson University
A P P E N D I XCAffine The need for geometric Affine Matrix representation of the linear Homogeneous 3D form of the Affine THE NEED FOR GEOMETRIC TRANSFORMATIONSOne could imagine a computer graphics system that requires the user to construct ev-erything directly into a single scene. But, one can also immediately see that this wouldbe an extremely limiting approach. In the real world, things come from various placesand are arranged together to create a scene. Further, many of these things are themselvescollections of smaller parts that are assembled together. We may wish to define one objectrelative to another for example we may want to place a hand at the end of an arm.
into 3D vectors with identical (thus the term homogeneous) 3rd coordinates set to 1: " x y # =) 2 66 66 66 4 x y 1 3 77 77 77 5: By convention, we call this third coordinate the w coordinate, to distinguish it from the usual 3D z coordinate. We also extend our 2D matrices to 3D homogeneous form by appending an extra row and column, giving Scale ...
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